I am your instructor Prof Geske (guess-key) and am happy to welcome you to the course! Please explore the course webpage.
Welcome! This is your Math 430 instructor Prof Geske! I would like you to kindly do the following prior to your first lecture.
sent: Fri Aug 21
| Instructor | Office Hours Location | |
|---|---|---|
| Prof Geske | geske (at) usc (dot) edu | KAP 244A |
| Yijie Pan | yijiepan@usc.edu | Math Center (KAP 263) |
You are encouraged to attend the office hours of any instructor. To gain the greatest advantage from office hours I recommend preparing your questions in advance. If it is impossible for you to attend these office hours but would still like to meet: feel free to reach out to your instructor or TA to schedule an alternative time to meet.
| Time Start | Time End | Mon | Tue | Wed | Thu | Fri |
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| 12PM | 1PM | |||||
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| 3PM | 4PM | |||||
| 4PM | 5PM | Geske | ||||
| 5PM | 6PM | Geske | ||||
| 6PM | 7PM | Geske |
In this table you will find a pdf scaffold posted before each lecture, which we will fill in during class. Below each scaffold you will find a corresponding list of problems from the ☞MyOpenMath practice. You will also find posted, after each exam, solutions to that exam.
| Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|
| Aug 24 ☞ Lecture 01 (A1) A1: Q1-Q4 |
Aug 25 | Aug 26 ☞ Lecture 02 (A1) A1: Q5-Q9 |
Aug 27 Groupwork 1 |
Aug 28 Lecture 03 (A1A2) |
| Aug 31 Lecture 04 (A2) |
Sep 01 | Sep 02 Lecture 05 (A2) |
Sep 03 Groupwork 2 |
Sep 04 Lecture 06 (A2A3) |
| Sep 07 No Class |
Sep 08 | Sep 09 Lecture 07 (A3) |
Sep 10 Groupwork 3 |
Sep 11 Lecture 08 (A3A4) |
| Sep 14 Lecture 09 (A4) |
Sep 15 | Sep 16 Lecture 10 (A4A5) |
Sep 17 Groupwork 4 |
Sep 18 Lecture 11 (A5) |
| Sep 21 Lecture 12 (A5B1) |
Sep 22 | Sep 23 Lecture 13 (B1) |
Sep 24 Groupwork 5 |
Sep 25 Lecture 14 (B1) |
| Sep 28 Midterm A |
Sep 29 | Sep 30 Lecture 15 (B2) |
Oct 01 Groupwork 6 |
Oct 02 Lecture 16 (B2) |
| Oct 05 Lecture 17 (B3) |
Oct 06 | Oct 07 Lecture 18 (B3) |
Oct 08 No Class |
Oct 09 No Class |
| Oct 12 Retake A |
Oct 13 | Oct 14 Lecture 19 (B4) |
Oct 15 Groupwork 7 |
Oct 16 Lecture 20 (B4) |
| Oct 19 Lecture 21 (B5) |
Oct 20 | Oct 21 Lecture 22 (B5) |
Oct 22 Groupwork 8 |
Oct 23 Lecture 23 (C1) |
| Oct 26 Midterm B |
Oct 27 | Oct 28 Lecture 24 (C1) |
Oct 29 Groupwork 9 |
Oct 30 Lecture 25 (C2) |
| Nov 02 Lecture 26 (C2) |
Nov 03 | Nov 04 Lecture 27 (C3) |
Nov 05 Groupwork 10 |
Nov 06 Lecture 28 (C3) |
| Nov 09 Retake AB |
Nov 10 | Nov 11 No Class |
Nov 12 Groupwork 11 |
Nov 13 Lecture 29 (C4) |
| Nov 16 Lecture 30 (C4) |
Nov 17 | Nov 18 Lecture 31 (C5) |
Nov 19 Groupwork 12 |
Nov 20 Lecture 32 (C5) |
| Nov 23 Midterm C |
Nov 24 | Nov 25 No Class |
Nov 26 No Class |
Nov 27 No Class |
| Nov 30 Lecture 33 (finalonly) |
Dec 01 | Dec 02 Lecture 34 (finalonly) |
Dec 03 Groupwork 13 |
Dec 04 Retake ABC |
| Dec 07 No Class |
Dec 08 No Class |
Dec 09 Final Exam |
The content of this syllabus is subject to change.
| Section | Time | Location |
|---|---|---|
| 39651 | MWF 2-2:50pm | KAP 163 |
The textbook is recommended but not required.
| Textbook | Author | Edition |
|---|---|---|
| Elementary Number Theory | Burton | 6th |
This course is broken up into Unit A, Unit B, and Unit C. Each unit consists of 5 topics. For a total of 15 topics. There is also a topic that is exclusive to the final.
| Topic | Name | Description |
|---|---|---|
| A1 | Induction and Binomial Theorem | Use the principles of mathematical induction. Use the binomial theorem. Use properties of binomial coefficients. |
| A2 | Divisibility, Gcds, and Lcms | Use the division algorithm. Use properties of divisibility and gcds and lcms. |
| A3 | Euclidean Algorithm and Diohpantine Equations | Use the Euclidean algorithm to find gcds. Solve diophantine equations. |
| A4 | Primes and Fundamental Theorem of Arithmetic | Use the fundamental theorem of arithmetic. Prove variations of the fundamental theorem. Use the Sieve of Eratosthenes. |
| A5 | Sequences of Primes | Prove results related to infinitudes of primes in sequences of particular types. |
| B1 | Modular Arithmetic | Calculate residues and assess divisibility using modular arithmetic. |
| B2 | Linear Congruences and Chinese Remainder Theorem | Solve linear congruences. Use the Chinese remainder theorem. Prove results relating to the two. |
| B3 | Fermat's Little Theorem | Use Fermat's Little Theorem. Prove related results. Identify pseudoprimes. |
| B4 | Wilson's Theorem | Use Wilson's Theorem and its corollary on square roots of negative one. Prove related results. |
| B5 | Number Theoretic Functions | Use and prove results related to the tau and sigma functions. Prove results about number theoretic functions. |
| C1 | Mobius Inversion and Convolutions | Use and prove results related to convolutions and the Mobius inversion formula. |
| C2 | Floor Function And Change of Base | Use and prove results related to the floor function. Calculate powers of primes dividing factorials. Do this working relative other bases. |
| C3 | Euler Phi Function | Use and prove results relating to the Euler Phi function. |
| C4 | Euler's Theorem | Use Euler's theorem and prove related results. Relate phi to convolutions. |
| C5 | Order and Primitive Roots | Prove results related to the order of an integer and primitive roots. |
| Final Only | Quadratic Reciprocity and Cryptography | Solve and prove results related to quadratic congruences. Use Euler's criterion and Legendre symbols to consider quadratic residues. Prove results related to quadratic reciprocity. Interpret cryptographic schemes using number theory. |
Grading is broken up into Topic Mastery, PollEverywhere, Discussion Group Work, and the Final Exam.
| Category | Weight Total | Quantity of Items in Category | Weight Per Item |
|---|---|---|---|
| Topic Mastery | 60% | 15 topics | 4% per topic |
| Discussion: Groupwork | 10% | [13 groupworks - lowest 2 dropped] = [11 counted groupworks] | ~0.91% per counted groupwork |
| Lecture: PollEverywhere | 5% | [~2 polls per lecture - lowest 10 droppped] = [~60 counted polls] | ~0.08% per counted poll |
| Final Exam | 25% | 1 exam | 25% |
There are 15 topics (A1-A5, B1-B5, C1-C5) which were listed earlier in the syllabus.
Individual Topic Grading. Each topic is graded out of 4 points. 4 points indicates mastery. Topic grading will be assessed using Midterms and Retakes.
| Date | Assessment | Time | Location |
|---|---|---|---|
| Mon 9/28/26 | Midterm A | Your Lecture Time | Your Lecture Classroom |
| Mon 10/12/26 | Retake ≤A | Your Lecture Time | Your Lecture Classroom |
| Mon 10/26/26 | Midterm B | Your Lecture Time | Your Lecture Classroom |
| Mon 11/9/26 | Retake ≤B | Your Lecture Time | Your Lecture Classroom |
| Mon 11/23/26 | Midterm C | Your Lecture Time | Your Lecture Classroom |
| Fri 12/4/26 | Retake ≤C | Your Lecture Time | Your Lecture Classroom |
Each Midterm is tied to a unit and will have a single problem (with parts) for each each topic in that unit. For example Midterm A is tied to Unit A and will have A1, A2, A3, A4, and A5 problems. Each problem will be graded out of 4 points, indicating your score on that topic. The only possible scores on a topic will be 0, 1, 2, 3, 3.5, and 4. A 3.5 is a temporary score, assigned for example for a small computational error that does not indicate a lack of mastery, and may be rounded up to a 4 per the details given in the section on regrade requests below.
Each Retake is tied to all units up to that point and will have a single problem (with parts) for each topic in that unit. For example Retake ≤B is tied to Unit A and Unit B and will have A1, A2, ..., A5, B1, B2, ..., B5 problems. Each problem will be graded out of 4 points, indicating your score on that topic.
Your final score on a topic will be the maximum of your scores on each assessment. For example if your scores on A3 were [A3 on Midterm A: 1 points] and [A3 on Retake ≤A: 2 points] and [A3 on Retake ≤B: 3 points] and [A3 on Retake ≤C: 2 points] then your final score on A3 would be 3 points, as this was the maximum of your scores. Note that this means, if you ever score 4 points on a topic in an assessment, then you are effectively done with that topic, at least until the final exam.
Midterm and Retake Guidelines. Calculators are not allowed on any Midterms or Retakes. Notes are not allowed on any Midterms or Retakes. You will be provided a ☞ reference sheet however.
Midterm/Retake Absences. Exams must be taken in--person on the specified day. The only exception is for Midterm C in the fall semester, which occurs during the week of Thanksgiving, which you may opt to take on the Friday before Thanksgiving instead, still in--person, in which case you must email your professor to arrange a time.
Otherwise, if you miss a midterm/retake for a valid and documented reason (e.g. sickness with a note from your doctor), then after the final exam has been graded, you may select up to 3 topics that appear on both that midterm/retake and on the final exam and, for each, replace your missing topic score on that midterm/retake with a substitute score from the final exam. Note that certain topics may not appear on the final exam, but you will not know which until the final exam has occurred. If you miss multiple midterms/retakes, the maximum total number of substitute scores from the final exam you can use is 5.
Regrade Requests. If you believe an error has been made in grading, a regrade request can be submitted through Gradescope. Regrade requests may also be used to round up a score of 3.5 up to a 4. To round a 3.5 up to a 4, in your Gradescope regrade reqeust, you must explain your error and how you would correct it. Regrade requests are due about one-and-a-half weeks after each assessment, except for Retake ABC, in which case the regrades will be due a little less than one week after the assessment. If a request to round up a 3.5 is not made by the deadline, your score will be rounded down to a 3.
Contribution to Final Grade. Topic Mastery counts for 60% of your final grade. Therefore each topic contributes 4% to your final grade.
Preparing for Midterms/Retakes. A list of practice problems for each topic is provided on ☞ MyOpenMath. The problems on the exams will be similar to problems that appear in this practice list. If you can rapidly solve the problems from the practice list, without hints, and are comfortable with the core concepts and techniques behind these problems, then you will be well-prepared for the exam. If I have taught the course before, you will also find compilation of past exams and retakes on ☞ MyOpenMath.
Note on Exam Length. The midterms tend to be long, so do not necessarily plan to complete every topic, as you can retry missed topics on a retake. I strongly recommend earning high scores on at least 3 topics. Consider this for example: if for each assessment you are able to obtain 3 new scores of 4/4 then you will have mastered every topic by the end of the semester.
Our sections will have a unique final exam not shared by other instructors.
| Date | Time | Location |
|---|---|---|
| Fri Dec 11 | 2-4pm | usual lecture classroom |
Final Exam Guidelines. Calculators are not allowed on the final exam. You will be provided a ☞ formula sheet for the final exam, and are not allowed other notes.
You may use generative AI freely at home to assist with your studies.
However, use of generative AI will be prohibited in the classroom, including both lecture and discussion. I believe that these short periods in AI–free zones will encourage you to train neural connections that will help you develop a more flexible understanding of the material and better prepare you for exams.
| Section | TA | Time | Location |
|---|---|---|---|
| 39652 | Yijie Pan | Th 3-3:50pm | KAP 163 |
Format. In discussion section you will work in groups of 3 or 4 to complete an assigned set of problems. Each group will have a randomly selected scribe who will write (on physical paper) and submit work on behalf of the group. Each groupwork will be out of 10 points total: 8 points will be assigned for obtaining correct answers with correct work, while the remaining 2 points will be assigned for presentation and style: is the work presented clearly organized, and is terminology used precisely? (Don't worry, you are not evaluated on the quality of your handwriting, provided your handwriting is, at the very least, legible.) Your TA will be present to assist your group, and can indicate to you what is expected in terms of presentation and style.
Guidelines. It is not possible to work alone, as part of the intention is to train collaboration. All groupwork must be completed and submitted during discussion section. You will submit groupwork through Gradescope, only after your TA has signed off on your submission, and to your TA. It is not possible to earn credit by completing groupwork outside of discussion section, where generative AI use cannot be monitored, as generative AI use is strictly prohibited in the classroom.
Contribution to Final Grade. Discussion groupwork will be worth 10% of the final grade. There will be a groupwork each discussion section, except, in the fall semester, the week of Thanksgiving, and the lowest 2 groupworks are dropped. These drops are intended to account for any reason you may need to miss a discussion section, including sickness or personal emergency.
Format. During lecture you will asked to respond to roughly 2 multiple choice polls related to the content currently being taught. You wil provide an answer within the specified time limit using the PollEverywhere application, which you may initially access through its tab on ☞ Brightspace. You will receive 75% of the credit merely for an attempt, and the remaining 25% for providing the correct answer.
Guidelines. You must attend lecture in person to complete a poll. As indicated earlier, AI use is not permitted in the classroom. The purpose of the poll is to encourage you to seriously think about the lectured content, and should feel low-stakes due to 75% of the credit being earned merely by answering.
Contribution to Final Grade. Lecture polls will be worth 5% of the final grade. There will be roughly 2 polls each lecture, and the lowest 10 poll scores will be dropped. These drops are intended to account for any reason you may need to miss lecture, including sickness or personal emergency. As indicated, you must attend lecture in person in order to complete the poll.
Each lecture will be accompanied in the ☞ Daily Schedule by a corresponding set of problems from the ☞ MyOpenMath practice. These suggested problems are not to be submitted, and their solutions will eventually be revealed. However, exam problems will largely be similar to select practice problems, so it would behoove you to study them after each lecture, so you are not overwhelmed in the days leading up to an exam.
These are an essential resource that often go underutilized. We encourage you to attend them to receive help on any aspect of the course. Find them in the ☞ Office Hours tab.
The ☞ USC Math Center (KAP 263) is a place to go if you want help with your math classes. It is open during regular business hours and is always stocked with graduate students who can assist you with your mathematics classes.
The University of Southern California is foremost a learning community committed to fostering successful scholars and researchers dedicated to the pursuit of knowledge and the transmission of ideas. Academic misconduct is in contrast to the university's mission to educate students through a broad array of first-rank academic, professional, and extracurricular programs and includes any act of dishonesty in the submission of academic work (either in draft or final form).
This course will follow the expectations for academic integrity as stated in the ☞ USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. You may not submit work written by others or "recycle" work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.
Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.
The impact of academic dishonesty is far-reaching and is considered a serious offense against the university and could result in outcomes such as failure on the assignment, failure in the course, suspension, or even expulsion from the university.
For more information about academic integrity see the ☞ student handbook or the ☞ Office of Academic Integrity's website, and university policies on ☞ Research and Scholarship Misconduct.
Zoom recordings of lecture will be provided and accessible through the Zoom tab on ☞ Brightspace.
USC has policies that prohibit recording and distribution of any synchronous and asynchronous course content outside of the learning environment.
Recording a university class without the express permission of the instructor and announcement to the class, or unless conducted pursuant to an Office of Student Accessibility Services (OSAS) accommodation. Recording can inhibit free discussion in the future, and thus infringe on the academic freedom of other students as well as the instructor. (☞ Living our Unifying Values: The USC Student Handbook, page 13).
Distribution or use of notes, recordings, exams, or other intellectual property, based on university classes or lectures without the express permission of the instructor for purposes other than individual or group study is not allowed. This includes but is not limited to providing materials for distribution by services publishing course materials. This restriction on unauthorized use also applies to all information, which had been distributed to students or in any way had been displayed for use in relationship to the class, whether obtained in class, via email, on the internet, or via any other media. (☞ Living our Unifying Values: The USC Student Handbook, page 13).
USC welcomes students with disabilities into all of the University’s educational programs. ☞ The Office of Student Accessibility Services (OSAS) is responsible for the determination of appropriate accommodations for students who encounter disability-related barriers. Once a student has completed the OSAS process (registration, initial appointment, and submitted documentation) and accommodations are determined to be reasonable and appropriate, a Letter of Accommodation (LOA) will be available to generate for each course. The LOA must be given to each course instructor by the student and followed up with a discussion. This should be done as early in the semester as possible as accommodations are not retroactive. More information can be found at ☞ osas.usc.edu. You may contact OSAS at (213) 740-0776 or via email at ☞ osasfrontdesk@usc.edu.
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